Please do NOT use any of those home remedies, you can easily kill your cats and dog.
Dish detergent is dangerous, it strips the oil fromt he skin, causes horrible allergies, and can get down the pet's throat and poison it.
Nothing else works except a topical flea preventative like Frontline or Advantage. There are products for dogs and products for cats.
You put this on the back of the animals neck, part the fur and put on skin. You do this every single month without fail, and you will have no more fleas.
Anything "cheap" or "natural" is at best a waste of time and money and at worst, can harm your animals - a lot.